Learn Finnish: Tuotko sinä mehua tänne? - Are you bringing juice here?

The dictionary form is tuoda. This is a Type 2 verb. To find the stem, you drop the -da, leaving the stem tuo- (which ends in a diphthong, a combination of two vowels). Then you add the personal ending for 'you' (-t) to get tuot (you bring). Finally, attaching the question particle -ko turns it into the question tuotko (are you bringing?).

Why is the word for juice written as mehua instead of mehu?

Mehua is in the partitive case, formed by adding -a to mehu. Finnish uses this case for uncountable things like liquids or food when you are talking about an unspecified amount. It translates to 'some juice' rather than 'the entire juice'.

What is the difference between tänne and täällä, which both translate to 'here'?

Finnish pays close attention to movement. You use täällä when something is stationary in a place (like 'I am here'). You use tänne when there is movement towards a place ('to here'). Since the action of bringing involves moving juice to this location, we must use tänne.

Do I have to include the word sinä (you) in this sentence?